Got Your Number
In the problem Got Your Number, students use number properties, number operations, organized lists, counting methods, and probability to solve problems. The mathematical topics that underlie the problem are number sense, number properties, addition, subtraction, multiplication, division, fractions, representations of rational numbers, counting principles, systematic charting, probability, and generalizations.In each level, students must make sense of the problem and persevere in solving it (MP.1). Each problem is divided into five levels of difficulty, Level A through Level E, to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.
PRE-K
In this task, students play a game with playing cards numbered 1-9. The object of the game is for the students to find pairs of cards that make 10.
LEVEL A
In this level, students are presented with a problem that involves summing three values. Their task involves picking three cards from five that were dealt in order to make a sum close to 20. The task is designed as a game for two students with the goal of keeping the difference from 20 as small as possible. Students conclude the game by describing their strategy.
Students will need to be fluent in adding and subtracting within 20 using mental strategies for this level (2.OA.B.2). They will use their mental strategies to help them select the cards that add closest to 20.
LEVEL B
In this level, their task involves picking four cards from six that were dealt in order to make two two-digit numbers whose sum is close to 100. The task is designed as a game for students with the goal of keeping the total difference from 100 as small as possible.
Students will use strategies based on place value in order to fluently add within 100 (2.NBT.B.5). Place-value strategies will help students make strategic decisions about what place to put a selected digit in, in order to make the sum close to 100.
LEVEL C
This level involves a game between two students. Each student has to create the largest possible three-digit number. When a card is picked, the student must place it in either the ones, tens, or hundreds place. Once a card is placed, it can’t be moved. Students play independently and can’t see one another’s cards until the end when they compare their numbers to determine which number is greater.
This level addresses Common Core standard 2.NBT.A.4 by having students compare 3-digit numbers. Students will use place-value understanding (2.NBT.A.1) in order to reason through what place to put each digit in, in order to create the largest number.
LEVEL D
In this level, students are asked to generalize their findings from Level C. Students are asked to predict and justify the best strategy for winning the game.
This level does not meet the standard explicitly, but it can be used as an extension of Common Core standard 2.NBT.A.1 by having students justify their strategies used in level C.
LEVEL E
In this level, students pick four one-digit numbers from a stack of cards. They will use these four digits to form two fractions. They also spin a spinner that identifies one of the four basic operations. They are asked to determine the equation that produces the smallest result using those four digits and apply the identified operation to form two fractions.
In this level, students apply their knowledge of the four operations with rational numbers (7.NS.A.3) to explain the strategy for winning a game (SMP 3). In the game, students must pick four one-digit numbers from a stack of cards. They will use these four digits to form two fractions. They also spin a spinner that identifies one of the four basic operations. They are asked to determine the equation that produces the smallest result using those four digits and apply the identified operation to form two fractions.
PROBLEM OF THE MONTH
Download the complete packet of Got Your Number Levels A-E here.
You can learn more about how to implement these problems in a school-wide Problem of the Month initiative in “Jumpstarting a Schoolwide Culture of Mathematical Thinking: Problems of the Month,” a practitioner’s guide. Download the guide as iBook with embedded videos or Download as PDF without embedded videos.
SOLUTIONS
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